If you keep LFS running for a longer time, will the "Core 0" temp raise any further? 55°C when idling is pretty high, but the thermal control of your lappy just might be set to keep your CPU at 55°C. Until your CPU temp exceeds 70°C you should be perfectly fine. Moreover, simple CPU overheat wouldn't make your computer crash.
Perhaps you could run some CPU stability tests just to make sure. Something like "CPU Burn-in" test ran for about 30 mins should do.
EDIT: What kind of graphics card does your computer have?
Perhaps you could run some CPU stability tests just to make sure. Something like "CPU Burn-in" test ran for about 30 mins should do.
EDIT: What kind of graphics card does your computer have?


Graphics driver update will not reduce CPU temp or it's load, but the info you've posted so far pointed me to a possible problem with it. Faulty graphics driver is very likely to cause crashes and image corruption like the one you get.